**Question:**

**It is a common observation that rain clouds** can be at about a kilometre altitude above the ground.

**(a) If a rain drop falls from such a height freely under gravity, what will be its speed? Also, calculate in km/h**

**(b) A typical rain drop is about 4 mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.**

**(c) Estimate the time required to flatten the drop.**

**(d) Rate of change of momentum is force. Estimate how much force such a drop would exert on you.**

**(e) Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5 cm.**

**Solution:**

(a) Velocity attained by the rain drop which is falling freely through the height h is:

v2 = u2 – 2g(-h)

As u = 0

v = √2gh = 100√2 m/s = 510 km/h

(b) Diameter of the drop, d = 2r = 4 mm

Radius of the drop, r = 2 mm = 2 × 10-3 m

Mass of the drop, m = Vρ = 3.4 × 10-5 kg

Momentum of the rain drop, p = mv = 5 × 10-3 kg.m/s

(c) Time required to flatten the drop is the time taken by the drop to reach the ground

t = d/v = 30 ms

(d) Force exerted by a rain drop is, F = change in momentum/time = p-0/t = 168 N

(e) Radius of umbrella, R = 1/2 m

Area of umbrella = 0.8 m2

No.of drops striking the umbrella, n = 320

Therefore the net force exerted = 54000N